The transformation of polynomial eigenfunctions of linear second-order difference operators: A special case of Meixner polynomials

Journal of Physics A: Mathematical and General

Volumn 34, Issue 28, 2001, Pages 5653-5666

  Bangerezako, G ^a   Hounkonnou, M N ^b  

^a Faculté des Sciences   (Central African Republic)

^b U de Rech en Phys Theor   (Benin)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035920025     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/28/303     Document Type: Article

References (31)

1. Akhiezer N I and Glazman I M 1966 Theory of Linear Operators in Hilbert Space (Moscow: Nauka) (in Russian)
2. Bangerezako G 1998 Discrete Darboux transformation for discrete polynomials of hypergeometric type J. Phys. A: Math. Gen. 31 1-6
3. Bangerezako G 1999 The factorization method for the Askey-Wilson polynomials J. Comput. Appl. Math. 107
4. Bangerezako G and Magnus A P 1999 The factorization method for the semi-classical polynomials Proc. Int. Workshop on Self-similar Systems (Dubna, 1998) JINR, E5-99-38, Dubna, ed V B Priezzhev and V P Spiridonov, pp 295-300
5. Bangerezako G 1999 PhD Thesis Dept. Math., Université Catholique de Louvain
6. Cooper F and Ginocchio J N 1987 Relationship between supersymmetry and solvable potentials Phys. Rev. D 36 8
7. Dubov S Yu, Eleonski V M and Kulagin N E 1992 Equidistant spectra of anharmonic oscillators Sov. Phys.-JETP 75 446
8. Ermolaeva O and Zhedanov A 1998 Spectral transformations and generalized Pollaczek polynomials Preprint
9. Jirari A 1995 Second-order Sturm-Liouville difference equations and orthogonal polynomials Mem. Am. Math. Soc. 113 542
10. Geronimus Ya 1940 On the polynomials orthogonal with respect to a given number sequence Reports of Researches Inst. Math. and Mech., Univ. Kharkov and Kharkov Math. Soc. T. XVII (in Russian)
11. Geronimus Ya 1940 On the polynomials orthogonal with respect to a given number sequence and a theorem by W Hahn Izv. Akad. Nauk. SSR Mat. 4 215-28 (in Russian)
12. Kalnins E G and Miller W 1989 Symmetry techniques for q-series: Askey-Wilson polynomials Rocky Mountain J. Math. 19 223-30
13. Kolmogorov A N and Fomin C V 1989 Elements of Theory of Functions and Functional Analysis (Moscow: Nauka) (in Russian)
14. Leonard D A 1982 Orthogonal polynomials, duality and association schemes SIAM J. Math. Anal. 13 656-63
15. Levai G 1989 A search for shape-invariant solvable potentials J. Phys. A: Math. Gen. 22 689-702
16. Levai G 1991 A class of exactly solvable potentials related to the Jacobi polynomials J. Phys. A: Math. Gen. 24 131-46
17. Magnus A P 1995 Special non uniform lattice (SNUL) orthogonal polynomials on discrete dense sets of points J. Comput. Appl. Math. 65 253-65
18. Magnus A P 1988 Associated Askey-Wilson polynomials as Laguerre-Hahn orthogonal polynomials (Springer Lecture Notes in Mathematics vol 1329) (Berlin: Springer) pp 261-78
19. Mielnik B 1984 Factorization method and new potentials with the oscillator spectrum J. Math. Phys. 25 3387-9
20. Miller W 1969 Lie theory and difference equations I J. Math. Anal. Appl. 28 383-99
21. Miller W 1989 Symmetry techniques and orthogonality for q-series IMA Vol. Math. Appl. 18 191-212
22. Nikiforov A, Suslov S and Uvarov V 1991 Classical Orthogonal Polynomials of a Discrete Variable (Berlin: Springer)
23. Oscar Rosas-Ortiz J 1998 Exactly solvable hydrogen-like potentials and factorization method J. Phys. A: Math. Gen. 31 10163-79
24. Oscar Rosas-Ortiz J 1998 On the factorization method in quantum mechanics Preprint quant-ph/9812003 Oscar Rosas-Ortiz J 1998 1st Int. Workshop on Symmetries in Quantum Optics (Burgos, 1998)
25. Oscar Rosas-Ortiz J 1998 On the factorization method in quantum mechanics Preprint quant-ph/9812003 Oscar Rosas-Ortiz J 1998 1st Int. Workshop on Symmetries in Quantum Optics (Burgos, 1998)
26. Pelez-Lorenzana A 1996 Factorization, ladder operators and isospectral structures Preprint quant-ph/9602003
27. Samsonov B and Ovcharov I 1995 Darboux transformation and non-classical orthogonal polynomials Izv. Vuzoff Fiz. 58-65 (in Russian)
28. Spiridonov V, Vinet L and Zhedanov A 1993 Difference Schrödinger operators with linear and exponential discrete spectra Lett. Math. Phys. 29 63-73
29. Spiridonov V, Vinet L and Zhedanov A 1997 Spectral transformations, self-similar reductions and orthogonal polynomials J. Phys. A: Math. Gen. 30 7621-37
30. Uvarov V 1969 The connection between systems of polynomials orthogonal with respect to different distribution functions USSR Comput. Math. Phys. 9 25-36
31. Zaitsev A and Leble S B 1999 Division of differential operators, intertwine relations and Darboux transformations Preprint math-ph/9903005